Paper 2021/056

The Study of Modulo $2^n$

Zhongfeng Niu

Abstract

In this paper, we present a new concept named the basic function. By the study of the basic function, we find the $O(n)$-time algorithm to calculate the probability or correlation for some property of Modulo $2^n$, including the difference-linear connective correlation coefficients, the linear approximation correlation coefficients, the differential probability, difference-boomerange connective probability, boomerange connective probability, boomerange-difference connective probability, etc.